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Geometric and analytic problems for a real submanifold in ℂn with CR singularities

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Abstract

In this survey article, we present some known results and also propose some open questions related to the analytic and geometric aspects of Bishop submanifolds in a complex space. We mainly focus on those problems that the author and his coauthors have recently worked on. The article also contains an example of a Bishop submanifold in ℂ3 of real codimension two, which cannot be quadratically flattened at a CR singular point but is CR non-minimal at any CR point. This provides a counter-example to a question asked in a private communication by Zaistev (2013).

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Acknowledgements

This work was supported by National Science Foundation of USA (Grant No. NSF-1363418).

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08903, USA

    Xiaojun Huang

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  1. Xiaojun Huang
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Correspondence to Xiaojun Huang.

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In memory of Professor LU QiKeng (1927–2015)

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Huang, X. Geometric and analytic problems for a real submanifold in ℂn with CR singularities. Sci. China Math. 60, 995–1004 (2017). https://doi.org/10.1007/s11425-016-9002-6

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